Show that the magnetic dipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital momentum $L$ of the electron by

$$M=\frac{e}{2 m} L.$$

Calculate the nuclear binding energy of the nucleus ${ }_{11}^{23} \mathrm{Na}$. The measured atomic mass of $\frac{23}{11} \mathrm{Na}$ is $22.989767$ amu.

A $13.0 \mathrm{~cm}$ diameter circular loop of wire is placed with the plane of the loop parallel to the uniform magnetic field between the pole pieces of a large magnet. When $3.80 \mathrm{~A}$ flows in the coil, the torque on it is $0.185 \mathrm{~m} \cdot \mathrm{N}$. What is the magnetic field strength?

Describe how eukaryotic cells are able to keep such large amounts of DNA in the small volume of the cell nucleus. (Hint Review the structure of a chromosome in Chapter 10.)

Thorium-231 is the product of alpha emission. It is radioactive and emits beta radiation. Determine (a) the parent nucleus of Th-231. (b) the daughter product of Th-231 decay.

What is the energy of the $\alpha$ particle emitted in the decay ${ }^{2104} \mathrm{Po} \rightarrow{ }^{206} \mathrm{~Pb}+\alpha$ ? Take into account the recoil of the daughter nucleus.

How many protons and how many neutrons are there in a nucleus of
(a) neon, $76 \mathrm{Ne}$
(b) zinc, 557 ( $\mathrm{Z}$
(c) silver, ${ }^{10} \mathrm{Ag}$.

Near the surface of the nucleus of a lead atom, the electric field has a strength of $3.4 \times 10^{21} \mathrm{~V} / \mathrm{m}$. What is the energy density in this field?

Give the number of protons and number of neutrons in the nucleus of each the following: (16.1) a. sodium-25 b. nickel-61 c. rubidium- 84 d. silver-110

Calculate the mass defect for the neon-20 nucleus. The mass of neon-20 is $19.992440 ~u$. (Hint: How many protons and neutrons does neon-20 have?)

Consider the beta decay ${ }^{10} \mathrm{Be} \rightarrow{ }^{10} \mathrm{~B}+\beta^{-}$, with the beryllium nucleus initially at rest. (c) What are the possible energies of that other particle?

A nucleus of 4 neutrons and 4 protons that is surrounded by 2 orbiting electrons is

(a) a positive ion.

(b) a negative ion.

(c ) an alpha particle

(d) a beta particle

Suppose an organism usually has 24 chromosomes in its nucleus. How many chromatids would it have just after the $S$ phase of the cell cycle?

An example of a "pick-up" nuclear reaction is $_{2}^{3} \mathrm{He}+ _{6}^{12} \mathrm{C} \rightarrow \mathrm{X}+\alpha .$ What is the resulting nucleus?